let n be Nat; :: thesis: for i being Element of n holds { p where p is n -element XFinSequence of NAT : p . i > 1 } is diophantine Subset of (n -xtuples_of NAT)
let i be Element of n; :: thesis: { p where p is n -element XFinSequence of NAT : p . i > 1 } is diophantine Subset of (n -xtuples_of NAT)
defpred S₁[ XFinSequence of NAT ] means 1 * ($1 . i) > (0 * ($1 . i)) + 1;
defpred S₂[ XFinSequence of NAT ] means $1 . i > 1;
A1: for q being n -element XFinSequence of NAT holds
( S₁[q] iff S₂[q] ) ;
{ q where q is n -element XFinSequence of NAT : S₁[q] } = { r where r is n -element XFinSequence of NAT : S₂[r] } from HILB10_3:sch 2(A1);
hence { p where p is n -element XFinSequence of NAT : p . i > 1 } is diophantine Subset of (n -xtuples_of NAT) by HILB10_3:7; :: thesis: verum